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Abstract

We discuss the empirical importance of long term cyclical effects in the volatility of financial returns. Following Amado and Teräsvirta (2009), ČiŽek and Spokoiny (2009) and others, we consider a general conditionally heteroscedastic process with stationarity property distorted by a deterministic function that governs the possible time variability of the unconditional variance. The function proposed in this paper can be interpreted as a finite Fourier approximation of an Almost Periodic (AP) function as defined by Corduneanu (1989). The resulting model has a particular form of a GARCH process with time varying parameters, intensively discussed in the recent literature. In the empirical analyses we apply a generalisation of the Bayesian AR(1)-GARCH model for daily returns of S&P500, covering the period of sixty years of US postwar economy, including the recently observed global financial crisis. The results of a formal Bayesian model comparison clearly indicate the existence of significant long term cyclical patterns in volatility with a strongly supported periodic component corresponding to a 14 year cycle. Our main results are invariant with respect to the changes of the conditional distribution from Normal to Student-tand to the changes of the volatility equation from regular GARCH to the Asymmetric GARCH.
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